标题： 具有预测器的分层嵌入自动编码器（HEAP）作为学习复杂多尺度物理系统长期演化的高效架构 显示英文标题

标题： Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems

摘要： 我们提出了一种新颖高效的架构，用于学习复杂多尺度物理系统的长期演化，该架构基于尺度分离的思想。 系统中动态出现的各种尺度的结构仅与其局部相互作用。 当处于接触状态时，相似尺度的结构可以直接相互作用；而当它们作为更大直接相互作用结构的一部分时，则可以间接相互作用。 这使得能够以高效的方式对多尺度系统进行建模，其中不需要对彼此远离的小尺度特征之间的相互作用进行建模。 分层全卷积自动编码器不仅像传统方法那样将物理系统的状态转换为单一嵌入层，而是将其转换为一系列嵌入层，这些嵌入层以对应分辨率级别保留各种尺度结构的空间信息。 较浅层在更精细的网格上嵌入较小的结构，而较深层则在较粗的网格上嵌入较大的结构。 预测器同步推进所有嵌入层。 通过组合卷积算子来模拟各种尺度特征之间的相互作用。 我们将模型的性能与传统的ResNet架构变体在Hasegawa-Wakatani湍流中的应用进行了比较。 观察到该系统的某些关键统计特性在长期预测精度方面有了多倍的提升。 显示英文摘要

摘要： We propose a novel efficient architecture for learning long-term evolution in complex multi-scale physical systems which is based on the idea of separation of scales. Structures of various scales that dynamically emerge in the system interact with each other only locally. Structures of similar scale can interact directly when they are in contact and indirectly when they are parts of larger structures that interact directly. This enables modeling a multi-scale system in an efficient way, where interactions between small-scale features that are apart from each other do not need to be modeled. The hierarchical fully-convolutional autoencoder transforms the state of a physical system not just into a single embedding layer, as it is done conventionally, but into a series of embedding layers which encode structures of various scales preserving spatial information at a corresponding resolution level. Shallower layers embed smaller structures on a finer grid, while deeper layers embed larger structures on a coarser grid. The predictor advances all embedding layers in sync. Interactions between features of various scales are modeled using a combination of convolutional operators. We compare the performance of our model to variations of a conventional ResNet architecture in application to the Hasegawa-Wakatani turbulence. A multifold improvement in long-term prediction accuracy was observed for crucial statistical characteristics of this system.